Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields

DOI10.1007/s10711-004-2454-3zbMath1067.14061OpenAlexW1973551129MaRDI QIDQ1775141

Chara Pantazi, Jaume Llibre

Publication date: 4 May 2005

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-004-2454-3

zbMATH Keywords

polynomial vector fieldsalgebraic limit cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Topology of real algebraic varieties (14P25)

Related Items (3)

Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers ⋮ On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems

Cites Work

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• Configurations of limit cycles and planar polynomial vector fields.
• A transfer principle in the real plane from nonsingular algebraic curves to polynomial vector fields
• On the nonexistence, existence and uniqueness of limit cycles
• Uniqueness of algebraic limit cycles for quadratic systems

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